QED Phenomena in an Ultrastrong Magnetic Field. II. Electron-Positron Scattering, $e^{\pm }$-Ion Scattering, and Relativistic Bremsstrahlung

Abstract

This paper continues the approach of Kostenko \& Thompson to calculating quantum electrodynamic processes in the ultrastrong magnetic field near some neutron stars, such as magnetars or merging binary neutron stars. Here we consider electron-positron scattering, the Coulomb scattering of electrons and positrons off ions, and relativistic $e^{\pm }$-ion bremsstrahlung. The evaluation of differential and total cross sections simplifies considerably when the magnetic field lies in the range $10^3{B}_{\mathrm{Q}}\gg B\gg B_{\mathrm{Q}}$, where $B_{\mathrm{Q}}\equiv m^2/e=4.4\times 10^{13}$ G. Then, relativistic motion of $e^{\pm }$ is possible even when restricted to the lowest Landau state. Accurate results for differential and total cross sections are obtained by truncating the sum over intermediate-state Landau levels and otherwise disregarding terms inversely proportional to the magnetic field, which are complicated enough to have inhibited previous attempts to calculate magnetic electron-positron scattering and relativistic bremsstrahlung. A quantitative account is made of the effects of Debye screening.

26 pages, 7 figures. Astrophysical Journal 2019, 875. Erratum added